Mathematical Sciences: Control and Stabilization Problems for a Class of Nonlinear Partial Differential

9402838 Russell这个项目涉及对Korteweg-de Vries和相关偏微分方程的全局(在状态空间)控制和稳定化问题的分析和计算研究。将同时考虑点(边界)和分布式控制模式。先进的计算和符号处理能力将被用于研究闭环过程的守恒律，以便获得解的先验界。这将允许仔细分析受控系统的暂态和渐近行为。Korteweg-de Vries方程和其他相关的非线性偏微分方程解的特征是包括孤立波，称为孤子。这些波出现在许多应用中，包括气象学和海洋学、光纤信号传输、化学传输和扩散过程以及许多其他应用。本项目研究将解决的问题包括孤立波中的能量衰减，孤立波的稳定产生，以及孤立波的中继器类型放大分析。这项研究将包括对被调查过程的数学分析和基于计算机的过程模拟。

9402838 Russell This project involves analytical and computational studies of global (in the state space) control and stabilization problems for the Korteweg - de Vries and related partial differential equations. Both point (boundary) and distributed control modes will be considered. Advanced computational and symbolic processing capabilities will be employed in the investigation of conservation laws for closed loop processes in order to obtain a priori bounds on solutions. This will permit a careful analysis of the transients and asymptotic behavior of the controlled system. Solutions of the Korteweg - de Vries, and other, related, nonlinear partial differential equations characteristically include solitary waves, called solitons. These waves occur in numerous applications, including meteorology and oceanography, fiber-optic signal transmission, chemical transport and diffusion processes, and many others. Questions of interest which will be addressed by the research to be undertaken in this project include energy attenuation in solitary waves, stable creation of solitary waves, and analysis of repeater type amplification of solitary waves. This research will include both mathematical analyses of the processes under investigation and computer based process simulation.